In a typical hydraulic fracturing treatment, fracturing treatment fluid comprising a transport slurry containing a solid proppant, such as sand, is injected into the wellbore at high pressures.
The transport of sand, as proppant, was examined in Biot and Medlin, “Theory of Sand Transport in Thin Fluids”, SPE 14468, Sep. 22-25, 1985, which is herein incorporated by reference. In Biot-Medlin, it was determined that the mechanics of sand transport are principally controlled by horizontal fluid velocity, U, of the transport fluid containing the proppant (transport slurry). The velocity ranges for transport mechanisms were defined in terms of the ratio vt/U as follows:                vt/U>0.9 Transport by rolling or sliding;        vt/U≈0.9 Critical condition of pick-up;        0.9>vt/U>0.1 Bed Load transport;        vt/U<0.1 Suspension transportwherein Vt is the terminal settling velocity for the transport slurry. Thus, at very low velocities, proppant moves only by sliding or rolling. The upper limit of this range is determined by a critical proppant pick-up velocity. At intermediate velocities, a fluidized layer is formed to provide bed load transport. At high velocities, proppant is carried by suspension within the transport fluid.        
Once natural reservoir pressures are exceeded, the fluid induces fractures in the formation and proppant is placed in the created fractures to ensure that the fractures remain open once the treating pressure is relieved. Highly conductive pathways, radiating laterally away from the wellbore, are thereby provided to increase the productivity of oil or gas well completion. The conductive fracture area is defined by the propped fracture height and the effective fracture length.
In the last years, considerable interest has been generated in recently developed ultra-lightweight (ULW) proppants which have the requisite mechanical properties to function as a fracturing proppant at reservoir temperature and stress conditions. Hydraulic fracturing treatments employing the ULW proppants have often resulted in stimulated well productivity well beyond expectations. ULW proppants are believed to facilitate improved proppant placement, thus providing for significantly larger effective fracture area than can be achieved with previous fluid/proppant systems. Improvements in productivity have been attributable to the increased effective fracture area from use of such ULW proppants.
In light of cost economics, there has also recently been a renewed interest in slickwater fracturing which uses relatively non-damaging fracturing fluids. The most significant disadvantage associated with slickwater fracturing is poor proppant transportability afforded by the low viscosity treating fluid. Poor proppant transport results in the tendency of proppants to settle rapidly, often below the target zone, yielding relatively short effective fracture lengths and consequently, steeper post-stimulation production declines than may be desired. Post-frac production analyses frequently suggests that effective fracture area, defined by the propped fracture height and the effective fracture length, is significantly less than that designed, implying either the existence of excessive proppant-pack damage or that the proppant was not placed in designated areal location.
Three primary mechanisms work against the proper placement of proppant within the productive zone to achieve desired effective fracture area. First, fracture height typically develops beyond the boundaries of the productive zone, thereby diverting portions of the transport slurry into non-productive areas. As a result, the amount of proppant placed in the productive area may be reduced. Second, there exists a tendency for the proppant to settle during the pumping operation or prior to confinement by fracture closure following the treatment, potentially into non-productive areas. As a result, the amount of proppant placed in productive areas is decreased. Third, damage to the proppant pack placed within the productive zone often results from residual fluid components. This causes decreased conductivity of the proppant pack.
Efforts to provide improved effective fracture area have traditionally focused on the proppant transport and fracture clean-up attributes of fracturing fluid systems. Still, the mechanics of proppant transport are generally not well understood. As a result, introduction of the transport slurry into the formation typically is addressed with increased fluid viscosity and/or increased pumping rates, both of which have effects on fracture height containment and conductivity damage. As a result, optimized effective fracture area is generally not attained.
It is desirable to develop a model by which proppant transport can be regulated prior to introduction of the transport slurry (containing proppant) into the formation and during stimulation. In particular, since well productivity is directly related to the effective fracture area, a method of determining and/or estimating the propped fracture length and proppant transport variables is desired. It would further be highly desirable that such model be applicable with ULW proppants as well as non-damaging fracturing fluids, such as slickwater.